• Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9 

      Yu, Yuyin; Kaleyski, Nikolay Stoyanov; Budaghyan, Lilya; Li, Yongqiang (Journal article; Peer reviewed, 2020)
      Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for ...
    • The differential spectrum of a ternary power mapping 

      Xia, Yongbo; Zhang, Xianglai; Li, Chunlei; Helleseth, Tor (Journal article; Peer reviewed, 2020)
      A function f(x)from the finite field GF(pn)to itself is said to be differentially δ-uniform when the maximum number of solutions x ∈GF(pn)of f(x +a) −f(x) =bfor any a ∈GF(pn)∗and b ∈GF(pn)is equal to δ. Let p =3and d =3n−3. ...
    • On equivalence between known families of quadratic APN functions 

      Budaghyan, Lilya; Calderini, Marco; Villa, Irene (Journal article; Peer reviewed, 2020)
      This paper is dedicated to a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to each ...
    • Optimal ternary cyclic codes with minimum distance four and five 

      Li, Nian; Li, Chunlei; Helleseth, Tor; Ding, Cunsheng; Tang, Xiaohu (Journal article, 2014-11)
      Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are ...